Virginia SOL 8.PFA.5.e
The Standard
Solve problems in context that require the solution of a multistep linear inequality in one variable.
Virginia Standards of Learning for Mathematics · The student will write and solve multistep linear inequalities in one variable, including problems in context that require the solution of a multistep linear inequality in one variable.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students turn a real situation with limits, fees, rates, or totals into a multistep inequality. They solve it, then interpret the solution in context, including whether the boundary is included and whether answers must be whole numbers.
What Mastery Looks Like
- Students identify the unknown, write an inequality with the correct comparison sign, and solve it using inverse operations. They check the boundary value and state a reasonable answer using the units and limits from the situation.
Common Misconceptions
- Students may treat “at most” as greater than, or “more than” as greater than or equal to. They may forget to reverse the inequality sign when multiplying or dividing by a negative number. They may report a decimal answer when the situation requires a whole number.
How to Assess It
- Use this exit ticket: “A gym charges $18 plus $7 per visit. You can spend at most $60. Write and solve an inequality, then explain the answer.”
Lesson moves
Ways to Teach It
Give groups budget cards, fixed-fee cards, and item-price cards, then have them build an inequality and find the greatest number of items.
Ask students to explain how “at least,” “no more than,” and “fewer than” change the inequality sign in three sample situations.
Play inequality match-up using cards with situations, equations, solution sets, and written interpretations that students must group correctly.
Have students compare two phone plans and write an inequality to determine when one plan costs less than the other.
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